How I Came to Write A Beginner's Guide to Constructing the UniverseBy Michael S. Schneider

Books by Michael S. Schneider

A Beginner's Guide to Constructing the Universe

Constructing The Universe Activity Books

Constructing The Universe DVD

As
a youngster schooled in the US during the 1950’s Sputnik
era
I was exposed to the sciences, including NASA
rocket launches,
facts about the moon and planets, kitchen
chemistry,
supermarket
encyclopedias
and Mr.
Wizard
on television, and became very interested in all kinds of scientific
wonders, with a passion for electricity and magnetism, chemistry
sets,
Erector
sets,
model
rocketry,
the microscope and Ripley’s
Believe
It Or Not
books. However, I wasn’t an exceptional math student.
Mathematics was mostly presented as the memorization of rules and
boring paper drill, but I kept up. Yet in my mid-teens I became
earnestly interested in the geometry of nature and began lifelong
research into the subject, not suspecting everywhere it would lead.
I remember pondering the same hexagonal shape found in the beehive,
quartz crystal and metal hex-nuts. I could understand how a crystal
grew mechanically in this precise geometry by accumulating atoms, but
how did bees know how to produce the pattern which holds more weight
of honey than, say, a checkerboard pattern? I wasn’t
comfortable with the “trial and error” explanation, and
even if it was in their DNA how did that knowledge of superior design
get there? And then there were spirals, particularly the logarithmic
spiral, appearing in atomic spin-outs, seashells, embryos, tails,
claws, my own fists, bathtub whirlpools, dust devils and swirling
leaves, tornados, hurricanes, solar systems and galaxies. I found
books about each of these subjects but kept looking for one book
which would put it all together and explain it in a unified way. I scoured libraries
wherever I travelled (this was long before the internet) and kept
notebooks of research. Living just outside New York City, the NY
Public Library
became my primary focus when, before computers, there was only a vast
card catalog. At that time (mid 1960’s) the most interesting
books which discussed my interests were written in heavy, dusty but
well-produced and often gilded volumes of the late 19th
and early 20th
centuries including The
Curves of Life
by Cook, On
Growth And Form
(the unabridged version contained an omitted chapter on Fibonacci
numbers!) by Thompson, Nature’s
Harmonic Unity
by Coleman, The
Geometry of Art and Life
by Matila Ghyka, and The
Elements of Dynamic Symmetry
by Jay
Hambidge.
Immediately I was plunged into the mathematics of various spirals,
the Fibonacci
numbers,
the marvelous Golden
Ratio,
the Platonic
and Archimedean
Solids and more. I subscribed to the newly published Fibonacci
Quarterly
and acquired many of their self-published books on the Fibonacci and
Lucas
numbers
and related subjects. The mathematics was mostly beyond me, but
steadily I grew into it. Formulas, proofs and equations became less
intimidating as mathematics seemed to be a kind of poetry written in
a cosmic, even sacred language.

Since
the age of seven I’d been interested in simple electric
circuitry and as a teen built some logic circuits described by Claude
Shannon,
using electromagnetic relays scavenged from old telephone switching
banks found in electronics junk shops which were around in those
days. In 1964 and ‘65 I visited the New
York World’s Fair
more than a dozen times, marveling at its techno-vision of the
future. At that time I communicated with Edmund
C. Berkeley
about the primitive but fascinating Brainiac
computer kit
I had purchased from him (I still have the manual). In 1966 I learned
to program an IBM 360 and a Philco 2000 computer in FORTRAN using
punch cards. Coincidentally, one of the first assignments, a standard
task, was to write a program generating the Fibonacci sequence. In
contrast to any techno-vision of the future I attended the Woodstock
Festival
in 1969.

Absorbed
in my research concerning the shapes of nature I decided to major in
mathematics at the Polytechnic
Institute of Brooklyn
to learn this language so that I wouldn’t be intimidated by any
mathematics I encountered. Further exposure to the history of
mathematics revealed a great world of mathematicians, scientists,
philosophers and artists, opening wide the doors of my interests in
all directions. I graduated with a B.S. Mathematics in 1972.

I
took the saying attributed to Pythagoras that “All is number”
and Galileo’s idea of a “Book of Nature” quite
literally:

“Philosophy
is written in that great book which ever lies before our eyes —
I mean the universe — but we cannot understand it if we do not
first learn the language and grasp the symbols, in which it is
written.
This book is written in the mathematical language, and the symbols
are triangles, circles and other geometrical figures, without whose
help it is impossible to comprehend a single word of it; without
which one wanders in vain through a dark labyrinth.”

I
deeply wanted to understand this language and kept looking for one
book which would explain it all to me, especially the significance of
the shapes of nature’s geometric alphabet: the circles,
spheres, triangles, squares, pentagons, hexagons, spirals and the
rest which become obvious around us when we simply look. It became
clear that shapes represent ideas and principles, and the simpler the
number the more pervasive it is throughout nature.

Most
people can feel why a circle represents unity, wholeness,
completeness, and aren’t too surprised when shown how it holds
more inside it than any other shape with the same perimeter. That is,
a round pizza can hold more toppings than triangles, squares,
rectangles or any other shaped pizza having the same length of crust.
Unity is all there really is, but polarity is required for any
creation, so One casts its own shadow and pretends
to be Two to generate the single digits:

The
number Two is clearly about polarity, division, opinion, contrast,
conflict, cooperation and creation. It was reviled in ancient times
for breaking unity yet has a crucial role in the cosmic creating
process. It takes two to create, from two parents to lighting a match
by friction, and the two legs of a geometric compass using one still
point to generate the infinitely many points of a circle. The Unity
broken by Two is restored in Three as we can see in a tripod or braid
of hair, the electron and proton balanced by the neutron, as the
conflict between two lawyers is resolved by a judge. And so it goes
with the simple numbers and their shapes, each expressing its
principles in ways only it can. Each number has a different
personality and they each play a variety of roles in this dynamic
cosmos just as a small group of actors can change their guises for
different situations, with just a few actors playing many roles. The
universe appears first as an alphabet of shapes forming patterns of
words into the sentences, paragraphs, chapters of a book, a great
play with great actors in great parts telling great stories. The full
company of actors, the numbers 1 through 12, naturally form four
groups:

First
Principles: 1 and 2Numbers of Structure: 3, 4, 6, 8 and
12Numbers of Life: 5 and 10Numbers of Mystery: 7, 9 and 11

The
more I learned, the more I felt annoyed that I wasn’t taught
this shape-language in elementary school. I certainly would have
appreciated math instruction better. So at age 20 I decided to
organize my research and write the book I was seeking, to share with
others in the simplest manner possible the marvelous knowledge I had
found. I drew inspiration from past researchers, and took the
approach of Renaissance priest Giordano
Bruno
who wrote about the numbers one through ten, the single digits and
the beginning of their next cycle, as universal principles. The
single digits, of which all numbers are composed, seemed to be a
complete approach which would leave nothing out. Ten, eleven and
twelve continue their principles. I wasn’t much of a writer and
gradually had to learn to build ideas in a logical, flowing natural
order. I found the process of writing to be challenging but charming,
and handwrote my manuscripts and illustrated them in the fashion of a
Medieval illuminated manuscript. I soon found that this was not what
publishers wanted to see, but I persevered, learning something from
each failed attempt at publication, all the while kept enlarging and
refining every new version.

Three
days after graduating college in 1972 my younger brother and I took a
few months to hitchhike across the USA from New York to California
and Oregon. Along the way I was fascinated by the leaf and branch
arrangements of the wide variety of plants I came across in various
ecologies across the continent. I delighted in verifying the
existence of Fibonacci phyllotaxis
and marveled at all the variations on one theme in this world of
living mathematics.

Since
1970 I had also been reading Ouspensky’s Tertium
Organum
and In
Search of the Miraculous,
along with Gurdjieff’s All
and Everything
where I was struck by the idea of legominisms, of a worldwide
heritage of art and monuments passing important knowledge through the
generations, whose message was understood through their symbolism and
proportions. I read Churchward’s The
Sacred Symbols of Mu
camped in the Colorado Rocky Mountains. In 1970 I had also come
across the writings of Vitvan,
an American master trained in the early 20th
century in the ancient Hindu tradition of meditation. His writings
provided deeper insight into this cosmos as a vast energy system and
the geometric language of nature which can be understood as
consciousness manifesting materially as geometric configurations of
units of energy, atoms. I think he’s correct in that each of
nature’s forms in this living cosmos, from crystals to flowers
to creatures, planets, stars and galaxies, is a geometric expression
revealing the state in which it’s conscious. Consciousness
itself is evolving, trailed by its form. I was amused to realize that
the words “matter” and “pattern” derive from
the Latin mater
and pater,
“mother” and “father” -- the cosmos takes the
form of matter in patterns; i.e., the Periodic Table of Elements,
etc. Through Vitvan I was also introduced to the longest and most
profound poem written in English, Savitri
by Sri Aurobindo Ghose, the astrological language of Biblical
symbolism in The
Restored New Testament
by James Morgan Pryse,
and Science
and Sanity
by Alfred
Korzybski
with his teachings of “General
Semantics”
and how the words we use and think with influence what we “see”.

In
Autumn 1972, back in New York City, I came across The
View Over Atlantis
and a year later City
of Revelation
by John
Michell,
and my understanding of the significance of numbers, and legominisms,
changed forever. He inspired me, and a great many people, to see the
ancient world’s monuments, mythologies, landscapes and
traditions anew. He
re-introduced the history and significance of feng-shui
and ley
lines,
and revealed our worldwide heritage of monuments as repositories of
mathematical and geodetic knowledge. He revived an appreciation of
the writings of both Plato and the writer
and researcher into anomalous phenomena
Charles
Fort,
of the idea of cultural enchantment and a living cosmos. And perhaps
most importantly he revealed the heart of the mathematical traditions
in his New
Jerusalem and Cosmological Circle diagrams,
keys to understanding the proportions of monuments, temples,
cathedrals, layouts of cities, placement of capitals and countries
and the proportions of the entire cosmos. It helps to realize that
the Greek word kosmos
means embroidery. I studied his two books closely.

In
1973 I moved to the warmer clime of northern Florida where I was able
to examine closely the geometry of the lush world of semi-tropical
plants, appreciate the warmth and dignity of Southern friends, and
earned a Master’s Degree in Mathematics Education, with an
emphasis on the hands-on math laboratory approach. The next year I
found myself teaching science and math in the new idea of a Middle
School. If you want to know if you really understand a subject, and
to learn how to lay out ideas in a simple, growing sequence, teach 11
to 13 year olds. I did that for a dozen years. Fortunately I had
leeway in what I taught and was able to introduce the Fibonacci
numbers and Golden Ratio to youngsters, showing them the marvels of
this mathematics and how to observe them in everyday plants. It was
as interesting and eye-opening to them as it had been to me. Most
importantly, I learned by teaching children how people in general
learn, and saw the importance of hands-on experiences in real-world
situations. I felt even stronger that a wider audience should know
about this great geometric language of nature and its connections
with human culture. In the late 1970’s the school acquired a
number of TRS-80 computers and a dot-matrix printer which improved my
ability to organize my writings and communicate ideas.

In
1977 I traveled to India for two months as part of a Fulbright-Hayes
grant taking public school teachers there to learn about India and
create lessons to teach that it wasn’t all elephants and
snake-charmers. My specialty was the ancient Indian sciences and
mathematics, particularly the astronomical
parks
with their variety of giant sundials, stardials and moondials. At the
time India had virtually no television and I got to see it as it must
have been for millennia. I studied the proportions of temples and
monuments, visited schools of traditional art (noting their geometric
textbooks) and came across interesting people and books which
discussed geometry, proportions and the ancient Hindu Vastu
Shastra
(“Science of Construction”) including The
Hindu Temple
by Stella Kramrisch,
and later Architecture,
Time and Eternityby
Snodgrass and the idea of the temple as symbol of the journey within.

After
a dozen years teaching in a Florida Middle School, in 1986 I returned
to New York City and after a stint in the background helping make TV
commercials I was fortunate to find work on educational projects for
the New
York Academy of Sciences,
which was was tremendous fun. My job was to wander around the city
and look for examples of science and mathematics the public would be
interested in. I delighted in the 250-million year old spiral fossils
in the limestone façade of Tiffany’s, the variety of
3-cornered cracks in the sidewalks and the spiraling steam rising
from mandala-like manhole covers. I often went with binoculars to the
107th
floor observation area of the south World Trade Tower and to its
110th
level top outside. (Filling the space between those floors I saw the
building’s immense concrete counterweight on its giant
springs.) From there I could watch birds rise in spirals over the
warm, black tar roofs of buildings, then sink in cooler spirals over
parks and trees, all without flapping their wings. I saw countless
water tanks atop buildings with their metal bands circling the old,
wooden, barrel-like cylinders in a pattern from top to bottom in
proportion to the increasing water pressure. Bringing science to the
public (with help from Mr. Wizard’s experiment designer) we
installed an electronic scale into the floor of the tourist elevator
of the south World Trade Center Tower to show by digital display how
everyone’s combined weight changes due to inertia when it
begins to move and then when it slows down. We also put on an
exhibition of the scientific-surreal paintings of Remedios
Varo.
It was wonderful work but stopped when the department closed.

For
the next few years I honed my skills by writing articles and regular
columns for youngsters in various Scholastic
magazines including DynaMath,
Science and Computers,
and Science
World,
including articles and posters about spirals, Fibonacci numbers and
design in nature. From
1986-87 I was the creator and writer of the weekly "Mother
Nature" segment at WNYC-FM radio on the popular live broadcast
"Kids
America"
program, where Mother Nature had a problem each week which were
solved with help from the call-in audience. Unfortunately, the
actress who played Mother Nature knew no science but wouldn’t
follow the script or take direction and sounded like a barfly but the
show ran a dozen episodes. In
1986 I also volunteered to run the office part time at the School of
Sacred Arts in Greenwich Village where I was able to attend classes
learning to paint Tibetan
tankhas,
studying Egyptian language and symbolism with artist Mark
Hasselriis
who became a friend, and Jean and Katherine LeMee who taught the
mathematics of the musical octave (numerically and geometrically) and
thus we sang the proportions of a cathedral. I electrified a painting
I made of Egyptian art (all the deities’ eyes were
light-sensitive) to play musical notes determined by the shadows of
passers by. Fate stepped in when I attended and taught classes in
Sacred Geometry at the New
York Open Center
which is where I first met JohnMichell
and through him Keith
Critchlow
and others involved with sacred geometry and its philosophical,
architectural and other significances. What I liked about this
British group was that they weren’t “new age” but a
continuation of the traditions of mathematics deriving from (pre-)
Egypt through Pythagoras and others including the cathedral builders.
This numerical philosophy is timeless and not composed by anyone but
is inherent in the universe and periodically re-discovered, and
that’s what they did, standing on the shoulders of Plato, the
Neoplatonic
philosophers
and others who pondered the essential nature of numbers and cosmos.

I
was absorbed by The
Great Pyramid
by Thompkins and its Stecchini
appendix was my first real introduction to historical
metrology,
followed by Berriman.
After that I read Serpent
In the Sky: The High Wisdom of Ancient Egypt
and The
Traveler’s Key to Ancient Egypt
and soon met the author, the symbolist Egyptologist John
Anthony West
at the NY Open Center, and appreciated his great realization of water
erosion around the Sphinx, and through him the writings of Schwaller
de Lubicz
and Lucy
Lamy.
John Michell and John Anthony West became close, lifelong friends and
colleagues. Through the “sacred geometry” lectures of
Keith Critchlow I found myself gravitating to the Cathedral
of St. John the Divine,
the world’s largest church (601 feet the length of a football
field plus a football) in upper Manhattan and its obscure, unique
Library of Sacred Geometry overseen by June Cobb. It was located up a
narrow, stone spiral stairway and along the triforium above the main
space. I visited so many times that I was given a key to its door and
spent many hours alone perusing its contents, which included the
papers and geometric models of Matila
Ghyka
donated by his son, and obscure writings I never came across in any
other library. I pored over and absorbed everything I could. I also
spent many hours there outside, observing the masons creating the
Cathedral, erecting
the structure and sculpting the statues.
Eventually I engaged in conversations with the master mason, Simon
Verity,
with whom I enjoyed discussing the
cathedral’s geometry.
He let me examine the cathedral’s large architectural
blueprints that the masons were following, including its exact
measurements which allowed me to understand even more deeply the
mathematical proportions of a cathedral (this one was designed in the
French tradition) and its geometric symbolism. I discerned the
geometry of the façade and the octagonal space comprising the
front patio and stairs to the street. It turned out that the large
rectangular block at the front entrance which he was about to carve
into a number of statues had the proportions of the square root of 3
and showed
him the ways it could be harmoniously subdivided,
as well as its intentionally placed relationships with the façade,
the door and the space in front of the cathedral. As a result he
organized the individual sculptures harmoniously with each other and
with the building and space before it. Hardly anyone knows that Simon
made the eyes of the line of sculpted personages each follow the
visitor up the stairs in their sequence, each looking at a key point
in the geometry then passing us to the next set of eyes, watching us
enter each step from the street up to the central front door. I have
also since learned to play Rithmomachia,
the “Battle of Numbers” or “Philosophers Game,”
the only game allowed to be played in the Medieval monastary schools
and cathedrals. (It was the model for Hesse’s Glass
Bead Game.)
I can understand why it was studied and played in cathedral settings
and among the educated of the Renaissance. It’s based on the
mathematics of the musical scale. Players advance numerically and
geometrically, building musical harmonies to convert the opponent.
The object of the game is not to destroy the opposite side but to
incorporate them into a grand musical harmony. Its players were
simultaneously studying simple mathematics and number theory, the
proportions of cathedrals and the musical composition underlying
Gregorian and other chants
based on pure Pythagorean tuning.
After six centuries the game disappeared when learning mathematics
went from a philosophical pursuit to its present business and
commercial orientation.

High
on my list of delights found in New York City at that time were
weekly dinners at the apartment of Charlie and Evelyn Herzer, who
were deeply involved in Egyptian studies and had an exceptional
Egyptian library. The conversations with Mark Hasselriis, John
Anthony West, Rolling Stone writer Jonathan Cott (when he came out
with Isis
and Osiris),
occasional curators from the Egyptian wing of the Metropolitan Museum
of Art (including James
P. Allen)
and a core of others were great and rollicking feasts of food, wine
and discussion, perhaps something like Plato’s symposia. At the
time I felt I developed enough insight into ancient Egypt to lead
public tours of the Egyptian
Wing at the Met,
discussing more than the usual tour guide would, instead focusing on
the symbolism of deities, colors, shapes, numbers, proportions and
more assembled in that great collection. I even led workshops
including
"Science in the Art Museum", "The Mathematics of
Islamic Art" and "Showing Children Harmony"
for
public school teachers in the Met’s
Education Department.

All
the while I was working on my book about the principles and
appearances in nature and culture symbolized by the numbers one
through ten, and began to develop a book proposal suitable for a
potential agent to represent. At that time, just before Windows first
appeared, I found full-time work as a computer consultant and
software trainer. I specialized in “desktop computing”
(PageMaker, Quark, Photoshop and CorelDraw) so that I could create my
own illustrations and learn to apply a professional look and layout
to my writings about numbers in order to attract a publisher. I
conducted classes for countless corporations, businesses and
organizations ranging from Revlon and MTV to the New York Times and
the United Nations where I taught for a year. I also spent a lot of
time teaching in both World Trade Towers. At one point I helped a
rabbi organize a database for studying the letter combinations of the
Torah in what became known as the Bible
Code.
During free time I alternated my writing with electronics projects,
having access to the old electronics junk shops found in those days
on Canal Street in Chinatown, now long gone. I mostly built
electronic musical instruments that could be played without touching
them except by shadow or proximity, including a flute played by
clouds moving through the sky, and a stringless guitar played by
breaking infrared beams.

I
had been calling my tentative book “Reading Nature’s
Patterns” or maybe “The Timeless Alphabet.” But on
a visit to John Michell in London around 1991 he came up with the
delightful name “The Beginner’s Guide To Constructing The
Universe” and offered to write its Preface, which gave me
greater inspiration to complete it. Over the years my stays at John’s
place in Notting Hill were unforgettable high points in my life. It
was his custom to stay up all night reading, studying and doing
geometric constructions with a compass which often turned into
watercolor
paintings
covering most every surface in his flat as they dried. There were
readings aloud from Plato, Fort and others, computing the size of the
small gold pyramidion once atop the Great Pyramid, discussing
historical metrology and geodetic measures, the proportions of
Jerusalem and Solomon’s Temple, the growing surge of crop
circles about which he published The
Cerealogist,
and so much more. I witnessed many rosy London dawns transformed by
John’s presence. We visited Keith
Critchlow’s school
where I met students using traditional geometric constructions to
produce timeless designs for art and architecture. At Glastonbury we
made measurements of architecture to verify his insights. Through
John I met Christine
Rhone,
co-author of Twelve-Tribe
Nations and the Science of Enchanting the Landscape,
still a friend, and also John
Neal
who developed
their findings
into his seminal book All
Done With Mirrors,
which solves modern confusion about metrology by showing all ancient
systems (with metric as the exception) to be interrelated with each
by simple fractions, themselves fractions of the Earth’s
dimensions, with its three diameters: polar, mean and equatorial. Who
or how someone mapped the dimensions of the entire planet in deep
antiquity to such an astonishing degree I don’t know, but
traditional
measures
worldwide demonstrate a knowledge of it and sophisticated
mathematical skills and understanding beyond what is accepted in
today’s orthodoxy. But some astute archaeologist will soon
realize the importance of Michell and Neal’s work in this area
and stop measuring sites in obfuscating meters but instead apply the
exact measures for cubits used by the ancient designers themselves,
now available through Neal’s various writings. Through them I
met John Martineau (“Miranda Lundy”) author and editor of
the important Wooden
Books
series. Other important books for understanding the tradition of
geometric composition in art include The
Painter’s Secret Geometry
by Bouleau and The
Power of Limits
by Doczi whose workshop I attended at the NY Open Center and Sacred
Geometry
by Robert
Lawlor
(who also translated Schwaller).

In the early
1990’s I taught a small group of students including artists and
others interested in nature’s geometric and symbolic language
in the loft of artist Buffie
Johnson who was a friend of Carl Jung and a student of Egyptology
and esoteric studies with Natasha
Rambova (the wife of Rudolph
Valentino), as was Mark Hasselriis. Finally, in 1992, through
luck and perseverance, and my agent John
Brockman, the proposal for A
Beginner’s Guide To Constructing The Universe
was purchased by HarperCollins and edited by Eamon
Dolan. I then spent two years working on it full-time which meant
writing from sunrise to noon or 2pm, after which I had lunch,
explored the city, met friends, pursued research and attended
workshops and events. A few times a week I’d stroll across
Central Park to the Metropolitan Museum of Art to study the art of
various cultures, noting examples of geometry, proportions and
symbolism. The book was published in November 1994, their first book
published completely digitally since I was able to deliver it on
small diskettes. My intention for the book was to share in a simple
fashion this research which excited me, digesting and translating
what I found for the non-mathematical reader, especially for those
people who don’t think they’re a “math person”
because their natural appreciation of the wonderful and inspiring
world of mathematics was stifled and smothered at an early age with
the paperwork of a standardized education with dry textbook
“problems” (even the name -- who needs more problems in
their life?), and memorizing without understanding, moving too
quickly and mired in pointless examples.

Instead,
educators would find teaching mathematics easier and fun (but for the
standardized requirements) by bringing out the natural excitement of
children which comes about when teaching math through the shapes,
patterns and proportions found in nature and in worldwide traditions
of art, architecture and technology. Reading nature’s geometric
language tells us what nature is doing in any situation. Is it going
for strength, stability, maximum area or minimum volume? If we
understand it’s language we can cooperate with this vast
energy-system in which we’re integrated and actually function.
In my opinion, learning mathematics through nature should be a basic
part of all elementary education. It should be an important part of
all environmental studies. I even expect that the simple language of
numbers, shapes and proportions will be handy to know someday to
communicate with intelligent alien life. Numbers and the principles
they represent are timeless. No one invented them, they came with the
universe and are all-pervading. Their symbolism arises naturally from
each number’s inherent nature, its simple arithmetic properties
and its relations with other numbers. That won’t ever change
and so it’s no wonder it’s always been the official
language of the cosmos. As I wrote, the universe may be a mystery,
but it’s not a secret. We can see its principles through the
study of numbers which are always the same and available to anyone at
any time in history. It seems to me that the most outstanding
characteristic of the cosmos is wisdom. As the most fundamental of
Plato’s archetypes, numbers are ambassadors from eternity here
to help teach this wisdom, showing us who we are and how best to live
in this dynamic, beautiful cosmos of wise design. It seems to me that
every citizen of this universe has a responsibility to be familiar if
not fluent in the language in which it’s all written.

My book
isn’t for everyone. If you’re expecting equations,
formulas and such abstractions you’ll be disappointed. Rather,
it’s about encouraging ordinary people not trained in
mathematics to look at the world for themselves through new eyes
provided by simple numbers. It’s an introductory education in
reading nature’s language, seeing the ways that simple numbers
pervade the designs of technology (have you noticed the geometric
variety of wheel rims lately?). Numbers inform every culture through
religion, mythology, folk tales, fairy tales, sayings and proverbs.

Over the
years I collected quotations relevant to numbers, their principles
and studies, some of which line the book’s wide margins.
They’ve turned out to be quite popular.

Through
a casual suggestion from my friend David
Fideler, publisher of The
Pythagorean Source Book and Library
and other traditional works of sacred geometry and perennial wisdom,
I found myself Dean of Mathematics and Dean of Science at the private
Ross School in
East Hampton, New York, during 1996-97. This fascinating experience
confirmed that even when a school has unlimited funds its true value
comes down to the teachers, their knowledge of the subject in as wide
an interconnected context as possible and most importantly having
inspiration and a love of learning to ignite their students. In 1996
David and I held a workshop where he audibly demonstrated the
mathematics of the Pythagorean musical octave and I presented a class
on the Fibonacci numbers in nature.

In the
nineteen years, one Metonic
cycle, that the book has been in print I’ve felt
satisfaction seeing its positive influence on teachers, students,
writers, artists and creative people in general, and in inspiring
people who didn’t think they could enjoy anything mathematical.
I was amused to hear a woman tell me that every day her ten year old
grandson climbed a tree to read the book in its branches.

For the past
16 years I’ve been living in northern California where I’ve
found a most receptive audience and so have offered classes and
workshops to young and old. For three years I had my own Constructing
The Universe Classroom for both adults and youngsters dedicated
to these studies of mathematics (especially geometric construction)
and its relations to nature, art, philosophy and symbolism. A useful
text for adults was John Michell’s posthumously published How
the World is Made: The Story of Creation According To Sacred
Geometry.
In these years I’ve also written a series of six Constructing
The Universe Activity Book workbooks offering hands-on activities
with a compass and straightedge upon images of nature and art to
reveal their openly-hidden proportions. Last year I came out with a
DVD titled A
Journey From 1 to 12 incorporating the fullest expression of
number interactions necessary to understand all the forms and
proportions of nature through the cosmos. It’s dedicated to
John Michell. For the past dozen years I’ve been teaching a
course called “Mathematical Ideas for Artists” at the
California College of the Arts in
San Francisco, California. When I tell people that I teach math to
art students the response is nearly universal: oh, those unfortunate,
sensitive art students, required to endure a dulling math class. But
when I explain that I teach about the proportions of nature, the
natural symbolism of numbers and shapes, and the ways that great
artists, architects and designers have used this very knowledge of
shapes and proportions to create universally beautiful works, most
people easily understand and recognize the rightness of this
approach. Rather than being rigid, it offers the artist harmonious
suggestions. I’m teaching it as Durer
might have. Students in the same class with differing majors from
furniture and fashion design to sculpture, ceramics, jewelry,
graphic, textile and industrial design, photography, illustration,
oil painting and architecture all find something perfectly applicable
to enrich and improve their different compositions. My delight over
these forty years of teaching has been to research and learn wherever
my interests go and then create educational materials to teach what
I’ve learned. The study of numbers, which I consider to be a
healing activity, allows the soul, as Plato said, to purify and
become a worthy vessel for wisdom to enter. I especially enjoy
teaching youngsters who, before they’re dulled by headucation,
naturally understand all this and are eager to learn about the gentle
mathematical language of reality. At the moment I’m working on
another DVD, this one showing teachers how to teach mathematics
through the plant world. I hope to follow it with a book about my
research into the intentional geometry and mythological language of
symbolic shapes and proportions apparently used to design Egyptian
art, crafts, architecture and monuments in keeping with ma’at,
maintaining the ideal natural order of cosmos through the righteous
and harmonious proportions of all things. In my spare time I enjoy
exploring this energy world with a metal detector.

Biography

Michael
S. Schneider has been an educator for four decades. He delights in
teaching about the intersections of nature, science, mathematics and
art.

He
has a Bachelor of Science degree in Mathematics from the Polytechnic
Institute of Brooklyn, and a Master's Degree in
Mathematics Education from the University of Florida.

He’s
taught youngsters in public and private schools at the Middle School
and Elementary school levels since 1974. In 1977, Michael was a
Fulbright-Hayes Scholar in India studying ancient mathematics and
sciences. He has been a computer consultant at the United Nations,
Nickelodeon, MTV, NY Times and many other corporations.

He
has worked for the New York Academy of Sciences, and wrote articles,
posters and teachers' editions for various Scholastic magazines.
Michael was the creator and writer of the weekly "Mother Nature"
segment at WNYC-FM radio on the popular live broadcast "Kids
America" program (1986-87). He's also held workshops for
educators at The Metropolitan Museum of Art in New York through their
Education Department including "Science in the Art Museum",
"The Mathematics of Islamic Art" and "Showing Children
Harmony".

Michael
is the author of "A Beginner's Guide To Constructing The
Universe: The Mathematical Archetypes Of Nature, Art and Science"
(HarperPerennial paperback 1995), six "Constructing
The Universe Activity Books," a
DVD “Journey From 1 to 12”
and numerous articles concerning mathematics and teaching mathematics
through nature, art science and philosophy. His website is
http://www.constructingtheuniverse.com/